Primitive normal completions of the affine plane II

Details Primitive normal completions of the affine plane II Primitive normal completions of the affine plane II

2011-10-31

arxiv.org/abs/1110.6914v1

Mathematics

Algebraic Geometry

Draft - Unpolished

Scientific paper

In this article we continue from \cite{sub2-1} the study of normal analytic compactifications of $\cc^2$ from the point of view of their associated pencils of jets of curve germs centered at infinity. If $\bar X$ is a normal analytic compactification of $\cc^2$ which is {\em primitive}, i.e.\ $\bar X \setminus \cc^2$ is irreducible curve, then we show that $\bar X$ is projective iff $\bar X$ is algebraic iff at least one of the jets in the associated pencil of jets of curve-germs can be represented by a planar curve with one place at infinity. As a result we show that there are primitive normal analytic compactifications of $\cc^2$ which are {\em not} algebraic. We give explicit criteria for determining if the primitive compactification corresponding to a jet of curve germs at infinity is projective or not.

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